Title: Non-Monotonic Transverse-Momentum Correlations in Au+Au Collisions at High Baryon Density

Abstract: Characterizing the QCD phase diagram at finite baryon density is a central goal of high-energy nuclear physics. Two-particle transverse-momentum correlations offer sensitivity to the system's bulk dynamics, thermalization, and possible critical fluctuations, and are constructed to suppress the leading effects of volume fluctuations. I present STAR measurements of the relative dynamical correlation in gold-on-gold collisions at center-of-mass energies per nucleon pair from 3.0 to 7.7 GeV from the fixed-target and collider programs, recently published in Physical Review Letters, combined with Beam Energy Scan Phase-I data to cover 3 to 200 GeV in a single consistent analysis. The correlations follow the approximate inverse-square-root participant scaling expected from independent particle-emitting sources over most of this range, and we identify a breakdown of that scaling at a center-of-mass energy per nucleon pair of 3.0 GeV, where the system is dominated by hadronic interactions throughout its evolution. In central collisions we observe a non-monotonic energy dependence with a significance of approximately five standard deviations relative to a monotonic reference — the first such observation as a function of collision energy. AMPT and Boltzmann–Langevin calculations do not reproduce this structure. I will discuss the analysis methods behind these results, including the scaling baseline and the significance procedure, and the non-critical mechanisms that must be controlled before a critical interpretation can be sustained. I will then turn to ongoing work that interprets the relative dynamical correlation as a measure of event-by-event temperature fluctuations, which relates it directly to the heat capacity of the produced matter. This provides a route from a correlation measurement to a textbook thermodynamic quantity: the heat capacity per particle across the beam energy scan, obtained without an explicit freeze-out volume. I will present a first extraction along these lines and compare it to earlier determinations from event-by-event effective-temperature distributions and to hadron-resonance-gas expectations, together with the contributions — collective flow and other non-thermal sources of mean transverse-momentum fluctuation — that must be subtracted before the extracted specific heat can be taken as thermodynamic.